Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations

Abstract

We study basic Dolbeault cohomology and find new Weitzenböck formulas on a transversely Kähler foliation. We investigate conditions on mean curvature and Ricci curvature that impose restrictions on basic Dolbeault cohomology. For example, we prove that on a transversely Kähler foliation with positive transversal Ricci curvature, there are no nonzero basic-harmonic forms of type $(r,0)$, among other results.

23 pages

References in corpus (1)

• Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4